Generalized diffusion equation with fractional derivatives within Renyi statistics

TL;DR

This paper derives a generalized diffusion equation incorporating fractional derivatives within the framework of Renyi statistics, using the Zubarev method and fractional Liouville equations, with the diffusion coefficient averaged over a power distribution.

Contribution

It introduces a novel generalized diffusion equation with fractional derivatives based on Renyi statistics and the Zubarev method, expanding the theoretical understanding of non-equilibrium processes.

Findings

Derived a new fractional diffusion equation within Renyi statistics

Implemented averaging of the diffusion coefficient using a power distribution

Extended the theoretical framework of non-equilibrium statistical mechanics

Abstract

By using the Zubarev nonequilibrium statistical operator method, and the Liouville equation with fractional derivatives, a generalized diffusion equation with fractional derivatives is obtained within the Renyi statistics. Averaging in generalized diffusion coefficient is performed with a power distribution with the Renyi parameter $q$.